Question

Suppose m varies directly with n and inversely with p. If m=10 when n=2 and p=5, the constant of proportionality is k= What is the value of m when n=1/5 and p=4?

a) k = 5
b) m = 2.5
c) m = 20
d) k = 2

Answer 1

The constant of proportionality is 25 and the value of m when n = 1/5 and p = 4 is 1.25.

None of the given options is correct

Step-by-step explanation:

To solve this problem, we can use the relationship given: m varies directly with n and inversely with p. This relationship can be expressed as the equation:

m = k * (n/p)

where m represents the value of m, n represents the value of n, p represents the value of p, and k is the constant of proportionality.

1. Calculating the constant of proportionality (k):

Given that when m = 10, n = 2, and p = 5, we can substitute these values into the equation to solve for k:

10 = k * (2/5)

To solve for k, we can multiply both sides of the equation by 5/2:

10 * (5/2) = k * (2/5) * (5/2)

25 = k

Therefore, the constant of proportionality (k) is 25. This indicates that when n/p is multiplied by 25, it will yield the value of m.

2. Calculating the new value of m:

Now, we need to find the value of m when n = 1/5 and p = 4, using the constant of proportionality (k) we just calculated.

m = k * (n/p)

m = 25 * (1/5)/(4)

Simplifying the equation:

m = 25 * (1/5 * 1/4)

m = 25 * (1/20)

m = 25/20

m = 5/4

m = 1.25

Therefore, the value of m when n = 1/5 and p = 4 is 1.25.

It appears that none of the provided options (b) m = 2.5, c) m = 20, or d) k = 2) match the correct answer based on the given relationships and calculations.